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Weighted fuzzy transform and its application for approximation of discrete functions by continuous functions

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2014年第5期26卷 2437-2444页

作者： Rafiezadeh, Rafie Abazari, Reza Islamic Azad Univ Ardabil Branch Young Researchers & Elite Club Ardebil Iran

Fuzzy transform is one of the modern theoretical tools in the area of fuzzy approximation and fuzzy modeling. In this paper we define direct and inverse weighted fuzzy transform for discrete functions. As one of many ... 详细信息

关键词： Approximate reasoning discrete function fuzzy transform weighted fuzzy transform

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A logarithmic method for eliminating binary variables and constraints for the product of free-sign discrete functions

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discrete OPTIMIZATION 2013年第1期10卷 11-24页

作者： Lu, Hao-Chun Fu Jen Catholic Univ Coll Management Dept Informat Management Sinjhuang City 242 Taipei County Taiwan

In this paper, a logarithmic method was developed to solve optimization problems containing the product of free-sign discrete functions (PFDF). The current deterministic methods used to handle these problems are based on the concept of continuous variables;therefore, the methods always transform the original model into another programming model (e.g., DC programming, convex programming) and solve them with a commercial solver. As the nature of a discrete variable is quite different from that of a continuous one, developing a novel method to address the above mentioned problems is necessary. This study proposes a concise and efficient method that linearizes PFDF term into a set of linear inequalities directly without redundant transformation. Further, the proposed method only requires the logarithmic numbers of binary variables and constraints. Numerical examples demonstrate that the proposed formulation significantly outperforms current approaches. (C) 2012 Elsevier B.V. All rights reserved.

关键词： discrete function Free-sign variables Mixed-integer non-linear programming

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Adaptive smoothing in associated kernel discrete functions estimation using Bayesian approach

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2013年第12期83卷 2219-2231页

作者： Zougab, N. Adjabi, S. Kokonendji, C. C. Univ Bejaia LAMOS Lab Bejaia Algeria Univ Franche Comte LMB UMR CNRS 6623 F-25030 Besancon France

This paper demonstrates that cross-validation (CV) and Bayesian adaptive bandwidth selection can be applied in the estimation of associated kernel discrete functions. This idea is originally proposed by Brewer [A Bayesian model for local smoothing in kernel density estimation, Stat. Comput. 10 (2000), pp. 299-309] to derive variable bandwidths in adaptive kernel density estimation. Our approach considers the adaptive binomial kernel estimator and treats the variable bandwidths as parameters with beta prior distribution. The best variable bandwidth selector is estimated by the posterior mean in the Bayesian sense under squared error loss. Monte Carlo simulations are conducted to examine the performance of the proposed Bayesian adaptive approach in comparison with the performance of the Asymptotic mean integrated squared error estimator and CV technique for selecting a global (fixed) bandwidth proposed in Kokonendji and Senga Kiesse [discrete associated kernels method and extensions, Stat. Methodol. 8 (2011), pp. 497-516]. The Bayesian adaptive bandwidth estimator performs better than the global bandwidth, in particular for small and moderate sample sizes.

关键词： associate kernel bandwidth cross-validation discrete function prior distribution

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Analytical method for optimum non-negative integer bit allocation

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IET SIGNAL PROCESSING 2016年第8期10卷 936-946页

作者： Hatam, Mahdi Masnadi-Shirazi, Mohammad Ali Firouzabad Inst Higher Educ Dept Elect Engn Firouzabad Iran Shiraz Univ Sch Elect & Comp Engn Dept Commun & Elect Shiraz Iran

The optimum bit allocation (OBA) problem was first investigated by Huang and Schultheiss in 1963. They solved the problem allowing the bits to be signed real numbers. Later, different algorithms were proposed for OBA problem when the bits were constrained to be integer and non-negative. In 2006, Farber and Zeger proposed new algorithms for solving optimum integer bit allocation (OIBA) and optimum non-negative integer bit allocation (ONIBA). None of the existing algorithms for OIBA and ONIBA problems end with an analytical solution. In this study, a new analytical solution is proposed for OIBA and ONIBA problems based on a novel analytical optimisation approach. At first, a closed form solution is derived for Lagrange unconstraint problem. Then, by removing the Lagrange multiplier, an analytical solution is obtained for OIBA and ONIBA problems. Using the selection and bisection algorithms, a low complexity algorithm is proposed for searching in a group of discrete functions which can reduce the computational complexity of the analytical solution. The complexity of computing the analytical solution is O(k) which is much lower than the complexity of existing ONIBA algorithms.

关键词： video coding data compression computational complexity optimisation optimum nonnegative integer bit allocation problem ONIBA problem OIBA problem OBA problem optimum bit allocation problem optimum integer bit allocation problem analytical optimisation approach Lagrange unconstraint problem Lagrange multiplier removal selection and bisection algorithm low complexity algorithm discrete function computational complexity reduction video frame compression

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Geometric properties estimation from discrete curves using discrete derivatives

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COMPUTERS & GRAPHICS-UK 2011年第4期35卷 916-930页

作者： An, Yi Shao, Cheng Wang, Xiaoliang Li, Zhuohan Dalian Univ Technol Sch Control Sci & Engn Dalian 116023 Liaoning Peoples R China

Accurate geometric properties estimation from discrete curves is an important problem in many application domains, such as computer vision, pattern recognition, image processing, and geometric modeling. In this paper, we propose a novel method for estimating the geometric properties from discrete curves based on derivative estimation. We develop derivative estimation by defining the derivative of a discrete function at a point, which will be called the discrete derivative. Similarly, the second and higher order discrete derivatives at that point are also defined, and their convergence is demonstrated by theory analysis. These definitions of the different order discrete derivatives provide a simple and reliable way to estimate the derivatives from discrete curves. Based on the discrete derivatives, classical differential geometry can be discretized, and the geometric properties are estimated from discrete curves by using differential geometry theory. The proposed method is independent of any analytic curve and estimates the geometric properties directly from discrete data points, which makes it robust to the geometric shapes of discrete curves. Another advantage of the proposed method is the robustness to noise because of the calculation characteristics of the discrete derivatives. The proposed method is evaluated and compared with other existing methods in the experiments with both synthetic and real discrete curves. The test results show that the proposed method has good performance, and is robust to noise and suitable for different curve shapes. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Geometric properties Differential geometry discrete function discrete derivative discrete curve Convergence analysis

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MEASUREMENT THEORY AND SIGNAL THEORY .1. INVESTIGATIONS ON THE FOUNDATIONS

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INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 1984年第1期10卷 15-26页

作者： VANDERZANDEN, J Laboratory for Aero- and Hydrodynamics Department of Mechanical Engineering Delft University of Technology Netherlands

The concept of a sensor with finite resolution is chosen as the cornerstone of a physical measurement theory. It is concluded that the concept of a band-limited channel is less appropriate for this purpose because it is defined with help of specific mathematical operators on functions that are defined on an infinite *** is shown that measurement in continuum physics requires transfer, transformation and transport of energy to, by, and through a sensor: a non-equilibrium process. As theory requires equilibrium for any measurement, a paradox arises. It is indicated that experimental physics avoids this paradox with help of a hierarchy of space and time scales. The definitions and propositions are formulated in a similar way in order to avoid this equilibrium/non-equilibrium *** equivalence of the various forms of energy, as stated by the first law of thermodynamics and verified by experimental physics, renders interpretation of physical measurement relatively *** are defined to be products of measurement. They are carriers of a finite amount of information. As the class of continuous functions generate an infinite amount of information, discrete functions are selected to represent sampled and digitized signals. If the sampling interval is of the order of the largest characteristic time scale of the total system, then little information is lost by digitization. The number of significant digits is related to the resolution of the sensor and of the other parts of the measuring instrument. A measuring instrument is shown to be composed of a chain or a set of chains of sensors.

关键词： Sensor with finite resolution equilibrium/non-equilibrium paradox energy information measuring instrument signal digitization discrete function

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TeDDy: Templated decision diagram library

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SOFTWAREX 2024年 26卷

作者： Mrena, Michal Kvassay, Miroslav Zaitseva, Elena Univ Zilina Fac Management Sci & Informat Univ 8215-1 Zilina 01026 Slovakia

discrete functions are an integral part of numerous areas of research in mathematics and computer science. Efficient processing of such functions in a computer requires an appropriate representation. A very effective representation is decision diagrams, which are suitable for software processing. In the paper, we present the Templated Decision Diagram Library (TeDDy), which implements Binary Decision Diagrams and Multivalued Decision Diagrams. These allow the efficient representation of Boolean functions, Multiple -valued logic functions, and integer functions. The library's core uses C++ language templates that enable a universal implementation for all types of diagrams offered without loss of runtime efficiency or duplication of code. The library consists of a module for the general manipulation of decision diagrams and a module that contains algorithms aimed at reliability analysis based on decision diagrams. Compared to other libraries, the added value of our library is in the second module dedicated to reliability analysis.

关键词： Binary decision diagram Boolean function discrete function Integer function Multi-valued decision diagram Reliability analysis

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A generalized multilevel-hybrid chaotic oscillator for low-cost and power-efficient short-range chaotic communication systems

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2020年第1期2020卷 1-14页

作者： Dukhan, Ammar Jayalath, Dhammika van Heijster, Peter Senadji, Bouchra Banks, Jasmine Queensland Univ Technol Sci & Engn Fac 2 George St Brisbane Qld Australia Al Mustansiriya Univ Coll Engn Elect Engn Dept Palestine St Baghdad Iraq

In this paper, we present and evaluate a novel multilevel hybrid-chaotic oscillator. The proposed generalized multilevel-hybrid chaotic oscillator (GM-HCO) was created by combining a multilevel discrete function generated from user data with a continuous function having a damping factor greater than ln(2) to achieve variable rates and adaptive carrier frequencies. Improved spectral efficiency and lower complexity of the transceiver compared with differentially coherent systems were achieved by multilevel signals at the transmitter and a matched filter at the receiver. An exact analytical solution for the generalized fixed basis function and the impulse response of the matched filter were also derived. The bit error rate (BER) expression of the GM-HCO was derived for two levels. It was found that the noise performance of the proposed system was better than a hybrid chaotic system based on forward time and differential chaos shift keying (DCSK). A comprehensive set of simulations were carried out to evaluate the performance of the proposed system with chaotic communication systems in the presence of additive white Gaussian noise (AWGN). The performance of the proposed system was comparable with that of conventional communication systems. The results demonstrate that the proposed system can offer better noise performance than existing chaotic communication systems, and it also offers variable transmitter frequencies and improved spectral efficiency. Noise-like behavior of the chaotic signals provides an additional layer of security at the physical layer compared with conventional (sinusoidal) communication systems.

关键词： Chaotic signal discrete function Hybrid chaotic system M-ary modulation Multilevel system Matched filter Generalized multilevel hybrid chaotic oscillator Reverse time Forward time

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Efficient finite difference analysis of microstructured optical fibers

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OPTICS EXPRESS 2005年第25期13卷 10349-10359页

作者： Kowalczyk, P Wiktor, M Mrozowski, M Gdansk Univ Technol Fac Elect Telecommun & Informat PL-80952 Gdansk Poland

A new technique of numerical analysis of microstructured optical fibers is presented. The technique combines a standard 2D finite difference equations with the discrete function expansion. By doing this one gets a matrix eigenvalue problem of a smaller size and a simple formulation of radiation boundary condition. The new algorithm was tested for the microstructures of different types and excellent agreement of the obtained results with other methods was achieved.

关键词： .boundary conditions smaller expansion OPEX eigenvalue difference microstructured optical fibers discrete function radiation boundary

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INVESTIGATIONS ON THE discrete PROLATE SPHEROIDAL SEQUENCE AT SHANNON SAMPLING RATE

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1983年第7-8期38卷 265-272页

作者： DELATOCNAYE, JLD CAVASSILAS, JF Laboratoire GESSY Université de Toulon et du Var Château Saint-Michel 83130 La Garde France

AnalyseLa représentation des signaux à bande limitée, échantillonnés en temps et observés sur une durée finie, conduit à privilégier des bases de dimension finie, appel... 详细信息

Analyse La représentation des signaux à bande limitée, échantillonnés en temps et observés sur une durée finie, conduit à privilégier des bases de dimension finie, appelées séquences sphéroïdales discrètes. L’obtention de telles bases est, d’un point de vue numérique, en général très délicate. On montre ici qu’un échantillonnage à la fréquence limite de Shannon peut fournir un algorithme très simple de calcul de ces séquences sphéroïdales dans le cas discret.

关键词： Signal theory Sampling Orthogonal function Spheroidal mode discrete function Band-limited signal Orthogonal sequence Finite duration Sampled signal

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